What's it about?

In 2006, we developed a new approach for image registration and motion estimation based on Markov Random Fields. On this website, you can download our software and test it for your own research and applications. From time to time, we will provide an updated version of the software including latest developments and/or new features.

Related Publications

Dense Image Registration through MRFs and Efficient Linear Programming

Authors: B. Glocker, N. Komodakis, G. Tziritas, N. Navab, N. Paragios

In this paper, we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context the registration problem is formulated using a discrete Markov Random Field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a small number of control points (registration grid) and an interpolation strategy. Then, the registration cost is expressed using a discrete sum over image costs (using an arbitrary similarity measure) projected on the control points, and a smoothness term that penalizes local deviations on the deformation field according to a neighborhood system on the grid. Towards a discrete approach the search space is quantized resulting in a fully discrete model. In order to account for large deformations and produce results on a high resolution level a multi-scale incremental approach is considered where the optimal solution is iteratively updated. This is done through successive morphings of the source towards the target image. Efficient linear programming using the primal dual principles is considered to recover the lowest potential of the cost function. Very promising results using synthetic data with known deformations and real data demonstrate the potentials of our approach.

Published in: Medical Image Analysis, Vol. 12, Issue 6, 2008

Approximated Curvature Penalty in Non-rigid Registration using Pairwise MRFs

Authors: B. Glocker, N. Komodakis, N. Paragios, N. Navab

Labeling of discrete Markov Random Fields (MRFs) has become an attractive approach for solving the problem of non-rigid image registration. Here, regularization plays an important role in order to obtain smooth deformations for the inherent ill-posed problem. Smoothness is achieved by penalizing the derivatives of the displacement field. However, efficient optimization strategies (based on iterative graph-cuts) are only available for first-order MRFs which contain cliques of size up to two. Higher-order cliques require graph modifications and insertion of auxiliary nodes, while pairwise interactions actually allow only regularization based on the first-order derivatives. In this paper, we propose an approximated curvature penalty using second-order derivatives defined on the MRF pairwise potentials. In our experiments, we demonstrate that our approximated term has similar properties as higher-order approaches (invariance to linear transformations), while the computational efficiency of pairwise models is preserved.

Published in: International Symposium on Visual Computing, 2009

Optical Flow Estimation with Uncertainties through Dynamic MRFs

Authors: B. Glocker, N. Paragios, N. Komodakis, G. Tziritas, N. Navab

In this paper, we propose a novel dynamic discrete framework to address image morphing with application to optical flow estimation. We reformulate the problem using a number of discrete displacements, and therefore the estimation of the morphing parameters becomes a tractable matching criteria independent combinatorial problem which is solved through the FastPD algorithm. In order to overcome the main limitation of discrete approaches (low dimensionality of the label space is unable to capture the continuous nature of the expected solution), we introduce a dynamic behavior in the model where the plausible discrete deformations (displacements) are varying in space (across the domain) and time (different states of the process - successive morphing states) according to the local uncertainty of the obtained solution.

Published in: IEEE Conference on Computer Vision and Pattern Recognition, 2008

Inter and Intra-Modal Deformable Registration: Continuous Deformations Meet Efficient Optimal Linear Programming

Authors: B. Glocker, N. Komodakis, N. Paragios, G. Tziritas, N. Navab

In this paper we propose a novel non-rigid volume registration based on discrete labeling and linear programming. The proposed framework reformulates registration as a minimal path extraction in a weighted graph. The space of solutions is represented using a set of a labels which are assigned to predefined displacements. The graph topology corresponds to a superimposed regular grid onto the volume. Links between neighborhood control points introduce smoothness, while links between the graph nodes and the labels (end-nodes) measure the cost induced to the objective function through the selection of a particular deformation for a given control point once projected to the entire volume domain. Higher order polynomials are used to express the volume deformation from the ones of the control points. Efficient linear programming that can guarantee the optimal solution up to (a user-defined) bound is considered to recover the optimal registration parameters. Therefore, the method is gradient free, can encode various similarity metrics (simple changes on the graph construction), can guarantee a globally sub-optimal solution and is computational tractable. Experimental validation using simulated data with known deformation, as well as manually segmented data demonstrate the extreme potentials of our approach.

Published in: Information Processing in Medical Imaging, 2007